Question three (20 points)

One scholar believes that the average height of boys and girls in sixth grade is

difference. The following table lists the students collected from two independent samples randomly selected by scholars.

Height (in inches):

Boys:

sample size(n1) : 10

Mean: 58.6

standard deviation(s1) : 13.45

Girls:

sample size(n2) : 10

Mean: 64.6

standard deviation(s2) : 11.15

a. At a significant level of 5% Is there evidence that the average height of boys and girls is different? What assumptions need to be set? (15 marks)

b. Repeat the test of the hypothesis in (a) above using the p-value method. (5 points)